1
$\begingroup$

I have a kalman filter like set up, when I get the current value of an observable process, and update my estimate of the state variable with it.

However, my observations are non-uniform in time, and I am trying to add the logic, that if the last observation was really long ago, I should forget about it, and use an a priori estimate X.

I can just switch to X, if time since the last observation is > T. But I was hoping to put in some general setting, which will be consistent with the Kalman filter logic. Does anyone have suggestions/references for it?

Many thanks.

| cite | improve this question | |
$\endgroup$
  • $\begingroup$ If you are observing $V_t, V_{t-1}, \ldots$ to update the system state $X_t$, why not observe $(V_t, V_{t-1})$ jointly and update the state only when $V_t = V_{t-1}$? $\endgroup$ – AdamO Apr 13 '16 at 18:26
  • $\begingroup$ Sorry, I don't understand your suggestion. Say, I have a stream of observations: 3 at t_1, 5 at t_2, 3 at t_3, 5 at t_4 - are you suggesting to ignore all of those? $\endgroup$ – LazyCat Apr 13 '16 at 18:34
  • $\begingroup$ And are you directly observing a state here? For instance, you observe 3 at time 1, but does that mean the state is 3 at time 1... the observations need not be the states, you could be observing acceleration in a vehicle and predicting its location on a road for instance. $\endgroup$ – AdamO Apr 13 '16 at 18:46
  • $\begingroup$ Yes, for simplicity, assume, that we are observing the state. $\endgroup$ – LazyCat Apr 13 '16 at 18:50
  • $\begingroup$ Then my example would not yield any valid state for the observations you present. $\endgroup$ – AdamO Apr 13 '16 at 18:51
0
$\begingroup$

If the Kalman filter-like model includes a covariance for the error-states, and if this covariance is being propagated in time such that it grows in the absence of new measurements, then a natural solution to the problem is to periodically check the trace of the error covariance against a ceiling threshold. If the threshold is exceeded we assume the filter has lost all useful information about the state, and that the state estimate should be reset to the a-priori value. Since the KF is usually a linearized approximation for a non-linear problem there is good reason to question the usefulness of the information stored in the covariance if the state error covariance is large.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.